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Revision as of 00:15, 1 August 2004
This is a list of calculus topics.
NB: the ordering of topics in sections is a suggestion to students.
Before calculus (pre calculus)
- Graph of a function
- Linear function
- Secant
- Slope
- Tangent
- Concavity
- Finite difference
- Radian
- Factorial
- Binomial theorem
- Free variables and bound variables
Limits
- Limit of a function
- Limit of a sequence
- Indeterminate form
- Table of limits
- Orders of approximation
- Trigonometric rational function
Differential calculus
- Derivative
- Notations
- Simplest rules
- Derivative (examples)
- Chain rule
- Product rule
- Quotient rule
- Inverse functions and differentiation
- Implicit differentiation
- Stationary point, maxima and minima
- Differential equation
- Differential operator
- Newton's method
- Taylor's theorem
- L'Hopital's rule
- Mean value theorem
- Logarithmic derivative
- Differential (mathematics)
Integral calculus
- Antiderivative, Indefinite integral
- Simplest rules
- Arbitrary constant of integration
- Fundamental theorem of calculus
- Integration by parts
- Inverse chain rule method
- Substitution rule
- Trigonometric substitution
- Partial fractions in integration
- A simple proof that 22/7 exceeds pi
- Trapezium rule
Special functions and numbers
- Natural logarithm
- E (mathematical constant)
- Exponential function
- Stirling's approximation
- Bernoulli numbers
Numerical integration
Lists and tables
- Table of derivatives
- Table of integrals
- Table of mathematical symbols
- List of integrals
- List of integrals of rational functions
- List of integrals of irrational functions
- List of integrals of trigonometric functions
- List of integrals of hyperbolic functions
- List of integrals of exponential functions
- List of integrals of logarithmic functions
- List of integrals of arc functions
- List of integrals of area functions
Multivariable
- Partial derivative
- Disk integration
- Shell integration
- Gabriel's horn
- Jacobian matrix
- Hessian
- Curvature
- Green's theorem
- Divergence theorem
- Stokes' theorem
Series
History
- Infinitesimal
- Gottfried Leibniz
- Isaac Newton
- Method of Fluxions
- Infinitesimal calculus
- Brook Taylor
- Colin Maclaurin
- Leonhard Euler
Nonstandard calculus
For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics.
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